Question

How many solutions does the system of equations have?

2x + 3y = 6

y= -2/3x-1

A.
0
B.
1
C.
2
D.
infinite

Answer 1

First, let's put them both in the same form, in this case, we'll do slope-intercept form.

2x-2x+3y=6-2x
3y=-2x+6
3y/3=-2x/3+6/3
y=-2/3x+2

So our two equations are:
y=-2/3x+2
and
y=-2/3x-1

The identical slopes tell us that these two lines are parallel, which means they will never intersect.

Therefore, your answer is 0.